CK-12-Calculus

5.4. Area of a Surface of Revolution http://www.ck12.org 5.4 Area of a Surface of Revolution Learning Objectives A student will ...

http://www.ck12.org Chapter 5. Applications of Definite Integrals Figure 20 Area of a Surface of Revolution Iffis a smooth and n ...

5.4. Area of a Surface of Revolution http://www.ck12.org Figure 21 The surface areaSis S= ∫b a^2 πy √ 1 + (dy dx ) 2 dx = ∫ 2 0 ...

http://www.ck12.org Chapter 5. Applications of Definite Integrals S= 2 π ∫ 145 1 u 1 / 2 du 36 =^236 π [ 2 3 u 3 / 2 ] 145 1 =^2 ...

5.4. Area of a Surface of Revolution http://www.ck12.org Simplifying, S=π ∫ 3 0 √ 4 y+ 1 dy. With the aid ofu−substitution, letu ...

http://www.ck12.org Chapter 5. Applications of Definite Integrals In problems #4–6 find the area of the surface generated by rev ...

5.5. Applications from Physics, Engineering, and Statistics http://www.ck12.org 5.5 Applications from Physics, Engineering, and ...

http://www.ck12.org Chapter 5. Applications of Definite Integrals A librarian displaces a book from an upper shelf to a lower on ...

5.5. Applications from Physics, Engineering, and Statistics http://www.ck12.org The graph ofF(x) = 80 − 2. 5 xrepresents the var ...

http://www.ck12.org Chapter 5. Applications of Definite Integrals 4.The bucket, the sand, and the rope together. Here we are ask ...

5.5. Applications from Physics, Engineering, and Statistics http://www.ck12.org The total pressure on the diver is the pressure ...

http://www.ck12.org Chapter 5. Applications of Definite Integrals Figure 24 Solution: Letx=the depth of the water. At an arbitra ...

5.5. Applications from Physics, Engineering, and Statistics http://www.ck12.org Normal Probabilities If you were told by the pos ...

http://www.ck12.org Chapter 5. Applications of Definite Integrals Figure 26 The Normal Probability Density Function The Gaussian ...

5.5. Applications from Physics, Engineering, and Statistics http://www.ck12.org P( 10 ≤x≤ 10. 5 ) = ∫ 10. 5 10 1 ( 0. 1 )√ 2 πe ...

http://www.ck12.org Chapter 5. Applications of Definite Integrals f( 9 ) =( 0. 1 )^1 √ 2 πe−(^9 −^10.^2 )^2 /(^2 (^0.^1 )^2 )dx ...

5.5. Applications from Physics, Engineering, and Statistics http://www.ck12.org That is, P( 85 ≤x≤ 115 )≈68%. Which says that 68 ...

http://www.ck12.org Chapter 5. Applications of Definite Integrals and Just Math Tutoring, Work and Hooke’s Law, Example 2 (6:52) ...

5.5. Applications from Physics, Engineering, and Statistics http://www.ck12.org Review Questions A particle moves along thex−ax ...

http://www.ck12.org Chapter 5. Applications of Definite Integrals Supposef(x)is the probability density function for the lifeti ...